# std::ranges::prev_permutation, std::ranges::prev_permutation_result

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< cpp‎ | algorithm‎ | ranges

Defined in header `<algorithm>` |  |
Call signature |  |
template< std::bidirectional_iterator I, std::sentinel_for<I> S, class Comp = ranges::less, class Proj = std::identity > requires std::sortable<I, Comp, Proj> constexpr prev_permutation_result<I> prev_permutation( I first, S last, Comp comp = {}, Proj proj = {} ); | (1) | (since C++20)
template< ranges::bidirectional_range R, class Comp = ranges::less, class Proj = std::identity > requires std::sortable<ranges::iterator_t<R>, Comp, Proj> constexpr prev_permutation_result<ranges::borrowed_iterator_t<R>> prev_permutation( R&& r, Comp comp = {}, Proj proj = {} ); | (2) | (since C++20)
Helper type |  |
template< class I > using prev_permutation_result = ranges::in_found_result<I>; | (3) | (since C++20)

1) Transforms the range `[`first`,` last`)` into the previous permutation, where the set of all permutations is ordered lexicographically with respect to binary comparison function object comp and projection function object proj.
Returns:

- {last, true} if "previous" permutation exists. Otherwise,
- {last, false}, and transforms the range into the (lexicographically) last permutation, as if by

    ranges::sort(first, last, comp, proj);
    ranges::reverse(first, last);

2) Same as (1), but uses r as the source range, as if using ranges::begin(r) as first, and ranges::end(r) as last.

The function-like entities described on this page are algorithm function objects (informally known as niebloids), that is:

- Explicit template argument lists cannot be specified when calling any of them.
- None of them are visible to argument-dependent lookup.
- When any of them are found by normal unqualified lookup as the name to the left of the function-call operator, argument-dependent lookup is inhibited.

### Parameters

first, last | - | the range of elements to "permute"
r | - | the range of elements to "permute"
comp | - | comparison function object which returns true if the first argument is less than the second
proj | - | projection to apply to the elements

### Return value

1) ranges::prev_permutation_result<I>{last, true} if the new permutation is lexicographically less than the old one. ranges::prev_permutation_result<I>{last, false} if the first permutation was reached and the range was reset to the last permutation.
2) Same as (1) except that the return type is ranges::prev_permutation_result<ranges::borrowed_iterator_t<R>>.

### Exceptions

Any exceptions thrown from iterator operations or the element swap.

### Complexity

At most \(\scriptsize N/2\)N / 2 swaps, where \(\scriptsize N\)N is ranges::distance(first, last) in case (1) or ranges::distance(r) in case (2). Averaged over the entire sequence of permutations, typical implementations use about 3 comparisons and 1.5 swaps per call.

### Notes

Implementations (e.g. MSVC STL) may enable vectorization when the iterator type models `contiguous_iterator` and swapping its value type calls neither non-trivial special member function nor ADL-found `swap`.

### Possible implementation

    struct prev_permutation_fn
    {
        template<std::bidirectional_iterator I, std::sentinel_for<I> S,
                 class Comp = ranges::less, class Proj = std::identity>
        requires std::sortable<I, Comp, Proj>
        constexpr ranges::prev_permutation_result<I>
            operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
        {
            // check that the sequence has at least two elements
            if (first == last)
                return {std::move(first), false};
            auto i{first};
            ++i;
            if (i == last)
                return {std::move(i), false};
            auto i_last{ranges::next(first, last)};
            i = i_last;
            --i;
            // main "permutating" loop
            for (;;)
            {
                auto i1{i};
                --i;
                if (std::invoke(comp, std::invoke(proj, *i1), std::invoke(proj, *i)))
                {
                    auto j{i_last};
                    while (!std::invoke(comp, std::invoke(proj, *--j), std::invoke(proj, *i)))
                        ;
                    ranges::iter_swap(i, j);
                    ranges::reverse(i1, last);
                    return {std::move(i_last), true};
                }
                // permutation "space" is exhausted
                if (i == first)
                {
                    ranges::reverse(first, last);
                    return {std::move(i_last), false};
                }
            }
        }

        template<ranges::bidirectional_range R, class Comp = ranges::less,
                 class Proj = std::identity>
        requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
        constexpr ranges::prev_permutation_result<ranges::borrowed_iterator_t<R>>
            operator()(R&& r, Comp comp = {}, Proj proj = {}) const
        {
            return (*this)(ranges::begin(r), ranges::end(r),
                           std::move(comp), std::move(proj));
        }
    };

    inline constexpr prev_permutation_fn prev_permutation {};

### Example

Run this code

    #include <algorithm>
    #include <array>
    #include <compare>
    #include <functional>
    #include <iostream>
    #include <string>

    struct S
    {
        char c{};
        int i{};
        auto operator<=>(const S&) const = default;
        friend std::ostream& operator<<(std::ostream& os, const S& s)
        {
            return os << "{'" << s.c << "', " << s.i << "}";
        }
    };

    auto print = [](auto const& v, char term = ' ')
    {
        std::cout << "{ ";
        for (const auto& e : v)
            std::cout << e << ' ';
        std::cout << '}' << term;
    };

    int main()
    {
        std::cout << "Generate all permutations (iterators case):\n";
        std::string s{"cba"};
        do print(s);
        while (std::ranges::prev_permutation(s.begin(), s.end()).found);

        std::cout << "\nGenerate all permutations (range case):\n";
        std::array a{'c', 'b', 'a'};
        do print(a);
        while (std::ranges::prev_permutation(a).found);

        std::cout << "\nGenerate all permutations using comparator:\n";
        using namespace std::literals;
        std::array z{"▁"s, "▄"s, "█"s};
        do print(z);
        while (std::ranges::prev_permutation(z, std::greater()).found);

        std::cout << "\nGenerate all permutations using projection:\n";
        std::array<S, 3> r{S{'C',1}, S{'B',2}, S{'A',3}};
        do print(r, '\n');
        while (std::ranges::prev_permutation(r, {}, &S::c).found);
    }

Output:

    Generate all permutations (iterators case):
    { c b a } { c a b } { b c a } { b a c } { a c b } { a b c }
    Generate all permutations (range case):
    { c b a } { c a b } { b c a } { b a c } { a c b } { a b c }
    Generate all permutations using comparator:
    { ▁ ▄ █ } { ▁ █ ▄ } { ▄ ▁ █ } { ▄ █ ▁ } { █ ▁ ▄ } { █ ▄ ▁ }
    Generate all permutations using projection:
    { {'C', 1} {'B', 2} {'A', 3} }
    { {'C', 1} {'A', 3} {'B', 2} }
    { {'B', 2} {'C', 1} {'A', 3} }
    { {'B', 2} {'A', 3} {'C', 1} }
    { {'A', 3} {'C', 1} {'B', 2} }
    { {'A', 3} {'B', 2} {'C', 1} }

### See also

ranges::next_permutation (C++20) | generates the next greater lexicographic permutation of a range of elements (algorithm function object)
ranges::is_permutation (C++20) | determines if a sequence is a permutation of another sequence (algorithm function object)
next_permutation | generates the next greater lexicographic permutation of a range of elements (function template)
prev_permutation | generates the next smaller lexicographic permutation of a range of elements (function template)
is_permutation (C++11) | determines if a sequence is a permutation of another sequence (function template)

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